为了提高随机截尾数据平均寿命的估计效率,采用平均秩思想,提出了基于排序集抽样方法的非参数估计量,证明了新估计量的渐近正态性,确定了其渐近方差,并与简单随机抽样下相应估计量进行了估计效率的比较,结果表明,排序集抽样效率高于简单随机抽样.最后,实际数据的应用结果验证了理论结果的正确性.
In order to improve the estimation efficiency of mean life for random truncated data, a nonparametric estimator based on ranked set sampling is proposed by adopting the idea of average rank. Its asymptotic normality is proved, and its asymptotic variance is identified. According to compare the new estimator with the corresponding estimator under simple random sampling, ranked set sampling is shown to be more efficient than simple random sampling. Finally, the application results of practical data verify the correctness of the theoretical results.
[1] CHEN Z H, BAI Z D, SINHA B K. Ranked set sampling-theory and application[M]. New York: Springer, 2004.
[2] 董晓芳,张良勇.排序集抽样下指数分布的产品可靠度研究[J].运筹与管理, 2020, 29(7): 99-104. DOI:10.12005/orms.2020.0177.
[3] ATA TUTKUN N, KOYUNCU N, KARABEY U. Discrete-time survival analysis under ranked set sampling: an application to Turkish motor insurance data[J]. J Stat Comput Simul, 2019, 89(4): 660-667. DOI:10.1080/00949655.2018.1564308.
[4] 董晓芳,张良勇,王志军.基于非均等排序集抽样的Wilcoxon符号秩检验[J].河北大学学报(自然科学版), 2020, 40(3): 225-231. DOI:10.3969/j.issn.1000-1565.2020.03.001.
[5] AWAIS M, HAQ A. A new cumulative sum control chart for monitoring the process mean using varied L ranked set sampling[J]. J Ind Prod Eng, 2018, 35(2): 74-90. DOI:10.1080/21681015.2017.1417787.
[6] RISCH N, ZHANG H. Extreme discordant sib pairs for mapping quantitative trait loci in humans[J]. Science, 1995, 268(5217): 1584-1589. DOI:10.1126/science.7777857.
[7] DELL T R, CLUTTER J L. Ranked set sampling theory with order statistics background[J]. Biometrics, 1972, 28(2): 545-555. DOI:10.2307/2556166.
[8] OZTURK O. Parametric estimation of location and scale parameters in ranked set sampling[J]. J Stat Plan Inference, 2011, 141(4): 1616-1622. DOI:10.1016/j.jspi.2010.11.019.
[9] BOCCI C, PETRUCCI A, ROCCO E. Ranked set sampling allocation models for multiple skewed variables: an application to agricultural data[J]. Environ Ecol Stat, 2010, 17(3): 333-345. DOI:10.1007/s10651-009-0110-7.
[10] BALCI S, AKKAYA A D, ULGEN B E. Modified maximum likelihood estimators using ranked set sampling[J]. J Comput Appl Math, 2013, 238: 171-179. DOI:10.1016/j.cam.2012.08.030.
[11] WANG X L, LIM J, STOKES L. Using ranked set sampling with cluster randomized designs for improved inference on treatment effects[J]. J Am Stat Assoc, 2016, 111(516): 1576-1590. DOI:10.1080/01621459.2015.1093946.
[12] 李涛,吴边.基于样本均值的最优无重叠k-序对排序集抽样[J].数学学报, 2017, 60(6): 897-910. DOI:10.3969/j.issn.0583-1431.2017.06.002.
[13] 崔利荣,赵先,刘芳宇.质量管理学[M].北京:中国人民大学出版社, 2012.
[14] 曹晋华,程侃.可靠性数学引论[M].2版.北京:高等教育出版社, 2006.
[15] GILL R. Large sample behaviour of the product-limit estimator on the whole line[J]. Ann Statist, 1983, 11(1): 49-58. DOI:10.1214/aos/1176346055.
[16] 董晓芳,张良勇.基于排序集抽样方法的可靠性估计[M].北京:科学出版社, 2021.
[17] LEE E T.生存数据分析的统计方法[M].2版.陈家鼎,戴中维,译.北京:中国统计出版社, 1998. (
